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Molecular dynamics of some crotonates using infrared band shapes
CHEMICAL
Volume 106. number 3
MOLECULAR
DYNAMICS
T.S. NATARAJAN,
PHYSICS LETTERS
USING INFRARED
OF SOME CROTONATES
J. GOWRIKRISHNA
Dcpnr~nrr~~r of Physics. hrdim hsrirurc
70 April 1983
BAND SHAPES
and J. SOBHANADRJ
of Tccl~rrolo~. Madras
600
036. fudio
Received 9 Dcccmber 1983;in final foml ?I I;ebruary 1984
Tbc dipole corrclstion function of three esters of crotonic acid have been ccmputrd from the infrared absorption bands. Both short-time and long-time behaviour of the correlation functions are computed and discussed. The correlation times xc also calculated. Thhc short-time behaviour was compared with the correlation functions generated as an even-power series with second and ;ourth moments. They were also compared with the correlation functions of the freely rotating molecule.
1. Introduction
frequency are generally dependent on all of these moments. The first moment can be used to locate the true frequency of the internal transitions. In the solvent-shift studies, this defines the shifted band origin. The second moment of a band is useful for calculating the average molecular rotational kinetic ener,,g. The higher-order momentsgive information about the intermolecular torques. At short times. the correlation function can be written as an even power series of the moments of the absorption band. In this paper, we present the results of the time correlation analysis carried out on the C-O stretch
Band-shape analysis of JR and Raman spectra provides information about the rotational motions of molecules and their intermolecular forces and torques in condensed phases [I-S]. Here the spectrum is considered as the Fourier transform of an appropriate time correlation function. Looking at the spectrum this way, one finds that on inversion one can get the time correlation function as a Fourier integral over the entire spectrum. By this, one can experimentally isolate the short-time and long-time behaviour of the correlation
function.
The
need
for such
[9]
a separation
stems from the fact that while the short-time behaviour of the correlation function may be discussed fairly rigorously in terms of the dynamics of the many-molecule system, at longer times the dynamics become too difficult and one has to rely on statistical arguments to establish the form of the correlation function. The advantage of looking at the spectra in the time-domain in terms of the correlation function instead of attempting to interpret the frequency spectrum directly is due to the reason that the intensity at any particular frequency includes contnbn>ans from the entire time development of the correlation function, that is, both the short- and long-time pars. In the case of a finite spectrum, the spectrum can be characterised uniquely by its moments. Any property of the spectrum such as the frequency at maximum intensity, the half-width, and the intensity at any 0 009-7614/84/S
(North-Holland
03.OCEl Elsevier Science Publishers Physics Publishing Division)
B.V.
and
the asymmetric
out-of-plane
deformation
of
bands of three crotonates in the pure liquids and in solution form. The second and fourth momentswcre cakulated from the band shapes. Also the first moment was determined to locate the shifted band origin. The correlation function behaviour of these compounds is compared with that of the classical ensemble of freely rotating molecules. The pupose of the present study is to understand the effect of the solvent, carbon tetrachloride in this case. on the solute and also to understand the short-rime and longtime behaviour of the molecule using the second and fourth moments calculated from the spectra. the methyl-group
[lo]
2. Experimental
The three compounds,
methyl.
ethyl and propyl 211
CHEMICAL
Volume 106. number 3
crotonates, were prepared and their purity was tested by measuring their boiling points, density and refractive index. The spectra for different concentrations were recorded with a Perkin-Elmer double-beam spectrometer (model PE983) at 27°C. The bands that are selected for the present study are not overlapped by the solvent (CC14) bands. The bands are centered at about 1186 cm- 1 for ethyl and propyl crotonates and at about 1378 cm-l for methyl crotonate. The spectra were recorded for a path length of 0.2 mm.
3. Computational
details
The dipole correlation functions from the expression [ 1 l] (u(O) -U(E)} =~i(w)
cos[(o
were computed
do ,
--w ($1
(1)
= I(w)(Jl(w)
dw) -’
(2)
is the normalised initial-state averaged transition probability at different angular frequencies. I(w) is given by WI
@I = a(4b
11- exp(-k&T)]
,
(3)
where u(o) is the absorption coefficient as a function of the angular frequency and is calculated from [ 131 T = To exp(-o
d) ,
0
where To is the incicient radiation and T is the transmitted radiation for a sample of thickness d. w. in expression (1) is the frequency of the band centre, i.e. the frequency of the vibrational transition of the isolated molecule. This is obtained from the first moment of the band [ 141:
The second and fourth moments [bZ(2) and fi1(4)] were calculated using the relations M(2) 212
=j-I(w)(w
- wo)2 dw ,
M(4) =Ji(o)
(w - w,-J4 dw .
(6)
Using these two, the short-time correlation function is expanded in an even power series as [ 1 1,151
1 - (1/2!)b1(2)t2
+(1/4!)hf(4)t4
+... (7)
The correlation function of a classical ensemble of freely rotating molecules is generally calculated in terms of reduced time units of (I/kT)‘I’. Here I is the moment of inertia, k is the Boltzmann constant and T is the temperature in kelvin. For 3 symmetric top [ 161 (prolate and oblate rotors) the moments of inertia about the three principal axes are considered. The expression used for CH,Cl, [ 171 (prolate rotor) is
(freely rotating)a
= exp[--$kT(l/Ib
where u(r) is the unit vector along the direction of the permanent dipole moment of the molecule at time r and I
20 April 1984
PHYSICS LETTERS
+ l/IC)r2]
.
For an asymmetric top, such as the crotonates considered in this paper, it would be easier to plot exp[-flf(2)t2/2] to represent the free rotor. A computer programme in Fortran TV language for the IBM 3701155 computer has been written to carry out the numerical calculations. The calculations were carried out for time intervals of 0.02 ps, over a total period of 2.0 ps, throughout the band-width, which is about 70-80 cm-l.
4. Results and discussion The time correlation analysis has been carried out on the C-O stretch band (z 1186 cm-l) of ethyl and propyl crotonates and on the asymmetric deformation of the methyl group (== 1378 cm-l) of methyl crotonate. The resultsare shown in figs. 14. In each figure, the correlation variation with 0.02 and 0.1 ps, time intervals are shown. Fig. 1 shows the correlation function variation for the three compounds in pure liquid form and figs. 24 show the concentration dependence. Apart from calculating the time correlation functions at various intervals, the correlation times and second and fourth moments were also calculated. The correlation functions have been calculated for two different time intervals (0.02 and 0.01 ps).
Volume
106, number
3
CHEMICAL
PHYSICS
20 April 1984
LETTERS
8 TIME
tps) (b) ~MCT(1378cri’ ECT (1186cm-1 -PCT (1185cm-’ --Free-rotor
2.0
-
TIMEtps) Fig. 1. Dipole
correlation functions for ethyl, methyl and propyl crotonates in pure liquid form are shown computed infrared absorption band at 1186 cm -’ for the ethyl and propyl crotonates and at 1378 cm -’ for methyl crotonare. ponds to correlation function variation with 0.1 ps time intervals and (b) for 0.02 ps intervals.
One common feature that can be observed in all these figures is that there is 2n initial curvature in the
from the (a) corres-
tributions from various processes to these bands are the same. The correlation functions in the case of
correlation function behaviour which is parabolic in
these two compounds decay faster than that in the
nature_ The time period of this initial curvature is different for different compounds. After this, the decay is essentially exponential.
case of methyl crotonate.This implies that in the ethyl 2nd propyi crotonates, the molecules undergo perturbation earlier t.lnvr in the methyl crotonate molccuie. This is understandable from the structures of rhese
4. I _ h-e
molecules.
liquids
The correlation function decay for the three compounds in pure-liquid form are shown in fig. 1. The correlation function variations in the case of ethyl and propyl crotonates are nearly the same except that it attains a small negative value in the case of propyl crotonate at longer times. This indicates that the con-
4.2. SoiLl tiOlU The correlation function decay for various concentrations of the three compounds in carbon tetrachloride solutions are shown in figs. 21. The correlation functions calculated for a classical ensemble of a freely 213
Volume
-CHEMICAL
106, number 3
20 April 1984
PHYSICS LETTERS
TIME
(ps)
(b)-40% ---
2 0% 60% Free-rotor
TIME (ps) Fig. 2. Dipole correlation function contours. The correlation function and (b) for 0.02 ps time intervals.
rotating
molecule
for methyl crotonate (in CQ) for four different concentrations obtained from the IR band for a freely rotating molecule is aLso shown. (a) corresponds to correlation function for 0.1
are also shown
In the case of methyl ps, the actual correlation
in figs 24.
crotonate, till a time of 1.I0 function is indistinguishable
from th’at of the freely rotating molecule (fig. 1). Later on, due to strong molecular collisions the actual correlation function falls of rapidly compared to that of the free rotor. In the case of ethyl and propyl crotonates, this value is 0.22 and 032 ps. The correlation function values corresponding to these times are O-64,0.79 and 0.67. We can estimate the approximate value of the angle through which the molecule makes free jumps. The actual value of the correlation function where the observed correlation function deviates 214
ps
from that of the free rotor is approximately equal to cos 0 where B is the parameter of interest [ 181. From this relation the angle through which the methyl,ethyl and propyl crotonate molecules make free jumps are obtained as 50°, 3S” and 48” respectively. There have been many reports on such estimations in the literature [ 17,181. It was assumed, in general, that molecular orientational motion occurs through small angles [ 191. Later it was observed that this type of diffusional behaviour does not take place in the case of liquids with small molecules such as Hz [20], CH4 [21] and NH3 1221. Even in the case of larger molecules the rotational steps are observed to be fairly large [23,17].
Volume
106, number
3
CHEMICAL
PHYSICS
20 April
LE’ITERS
1984
(ps)
TIME
&k&4-A+
20% 40%
7
60%
e ---
00%
Free-rotor
TIME (ps) Fig. 3. Dipolc correlation functions for ethyl crotonatc (in CC&) for four different concentrations obtained tours. The correlation function for a freely rotating molecule is also shown. (a) long-time and (b) short-time
As for the effect of the solvent concentration on the solute molecules, there is no effect on methyl crotonate molecules till about 0.16 ps. Similarly for ethyl and propyl crotonates it is 0.06 ps. The calculated correlation times for various concentrations are listed in table 1. The correlation times are generally increasing with increase in solvent concentration_ The correlation function calculated will have contributions from vibrational and rotational rekxation processes of the molecule. In order to separate these two one has to combine the infrared studies with Raman studies. The isotropic bandshape of the Raman scattering contains information about non-orientational motions of the molecule [%I] _
Table 1 Correlation times for various for the three crotonatrs Concentration
a)
(CCL)
100 80 60 40 70 10 a) In volume
from the IR band conbeha\iour.
concentrations
in
ccl4solution
~c methyl
ethyl
propyl
crotonste
croron3te
crotonixe
150 1.70 1.64 1.90 1.45
0.40 0.36 0.37 0.49 0.68 0.69
0.45 0.53 0.52. 0.53 0.87
percentage.
215
Volume 106:number 3
CHEMICAL
PHYSICS LE-ITERS
TIME
TIME
20 April 1984
(ps)
M eeecr -
20% 60% 00%
----
Fresrotor
(ps)
Fig. 4. Dipole correlation functions for propyl crotonaie (in CC&> for four different concentrations obtained from the IR band contours. The correlation function for a freely rotating molecule is also shown. (a) long-time and (b) short-time behaviour.
There are uncertainties in evaluating such correlation functions [IV]. (1) The correct baseline to use is often difficult to select. This difficulty arises due to the asymmetry of the band. (2) The vibrational relaxation processes contribute to the correlation times. (3) The perturbations due to hot bands. One way of avoiding the uncertainty in the baseline is to adjust the experimental second moment to the theoretical value by changing the base line. 4.3. Con-elation function for short times The correlation function is calculated using an evenpower series of the second [b!(2)] and fourth moments 216
[M(4)] for short times [ 1 I]. This way we can separate the short-time behaviour from the long-time behaviour. Substituting the calculated [M(3)] and [M(4)] values in the even-power series, the correlation functions are estimated and compared with the correlation functions calculated from the Fourier integral_ For methyl crotonate both these values agreeing upto a time of 0.9 ps and for ethyl and propyl crotonates upto 0.40 and 0.34 ps. For times higher than this, the neglect of higher-order moments is very much apparent. Since the higher-order moments are much more complicated, the computation of moments is difficult. Moreover, at long times the correlation function behaviour is exponential. So it cannot be generated using the evenpower series.
CHEhlICAL
Volume 106, nunlbcr 3
PHYSICS
From table I, one can see that the correlation times have approximately a linear dependence on solvent concentration. The following equations have been calculated by the least-squares method to represent the solvent concentration dependence of the correlation times (in ps): For methyl crotonate, rc = -0.57
“n + 2.08 _
For ethyl crotonates.
For propyl crotonate,
References [ I] R.G. Gordon, J. Chem. Phys. 44 (1966) 1630. [ 2 1 2. Gburski and W. Szezcpsnski. 5101. Phvs. 40 (1980) 649. [3] M.L. Bansal and A.P. Roy. Mol. Phvs. 38 (1979) 1419. 141 J.K. Vij. C.J. Reid. G.J. Evans, 51. Fermrio rmd Xl.\\‘. Evans, Advan. Mol. Rclau. Interaction Processes 22 (1982) 79. [S 1 S. Ikawa, 2;. Sate zmd M. Kimura. Chem. Phys. 47 (1980) 6.5. [6] J. McConnell, Rotxion brow&n moxion and diclec~ric
[9]
-0.07 xB + 0.56 ,
=
where xB is the solvent 100.
From these equations
1984
theory (Academic Press, New York, 1980). 17 ] W.G. Rorllschild, J. Chem. Phys. 65 (1976) 455. [8] R.G. Gordon. J. Chem. Phys. 39 (1963) 2788.
7, = -o.53_rB + 0.75 .
TC
20 April
LETTERS
concentration
in percentage/
we see that the dependence
calculated for methyl and ethyl crotonatesare parallel. and that their dependence is greater than that of propyl crotonate. With increase in dilution the correlation
of the molecule is retained for a longer time. But the correlation function decay isaway from the free rotor. This can be explained by considering the formation of a cage-like structure by the solvent molecules about the solute molecule. This kind of behaviour has been observed before in many systems like merhylene chlo-
ride molecules in polysterene [ 141, toluene in benzene [X] and pyridine in benzene [26]. From these observations, one can understand the effect of the non-polar solvent (carbon tetrachloride) on the solute molecules. From this study, we conclude that the orirntational motions of these molecules occur through large angles. The effect of the solvent on the solute molecules is clearly seen in this study.
Ados of spectral compounds. 2nd chaIt 5, p 332. [ 101 Atlas of spcctrrrl compounds, 2nd
datn and physical Ed., Vol.
1 (CRC
constsnrs
for organic
Press. Clewland)
dsta and physical constants ior orgonic Ed., Vol. 1 (CRC Press. Cleveland) chart 7. Esters and lactones, pp. 344 ff. [ 1 I ] W.G. Rothschild, J. Chem. Phvs. 49 (1968) 2250. [12j H.B.LevineandG.Bimbaum,Phys. Rev. 154(1967)56. [ 131 T.K.K. Srinivaan. J. Gowrikrishna and J. Sobhansdri, J. Mol. Liquids 26 (1983) 177. [ 141 \V.C. Rothschild, Macromolecules 1 (196s) 43. [ 15.1R.G.Gordon,J.Cbcm.Ph~s.43(1965) 1307. [ 16 1 W.G. Rothschild, J. Chem. Phps. 52 (1970) 6453.
! 171 \v.C. Roghschitd. J. Chcm. Phvs. 13 (1970) 990. [ 181 W.G. Rothschild, G.J. Rosasco and R.C. Livingsron. J. Chem. Phys.61(1975) 1253. [ 191 W.G. Rothschild, J. Chem. Phys.
53 (1970) 3265. [ 201 G.W. Hollernan and G.E. Ewing. J. Chem. Phvs. 47
(1967) 571. 121 l A. Cnbrorrr, R. Bardoux
and A. Chxnberland. Can. J. Chem. 47 (1969) 2915. 1221 P. Datts snd G.M. Bsrrow, J. Am. Chem. Sot. 87 (1965) 3053. [23] \V.G. Rothschild. J. Cbem. Phys. 51 (1969) 5187. [ 241 J.E. Griftiths. in: Vibrational spectra and structure, Vol. 6. ed. J.R. Durig (Elsevier, Amsterdam. 1977). [ 251 W. Reimschussel and H. Abramczyk, Cbem. Phys. Lcricrs 73 (1981) 565. (26 1 J. Gowrikrishn;l, T.K.K. Srinivaszn and J. Sobhanndri. J. Mol. Liquids, to be pubhshcd.
Acknowledgement The authors
are grateful
to Professor
S. Surjit Singh fadi-
for useful discussions and also for experimental ties.
217
Volume 106. number 3
MOLECULAR
DYNAMICS
T.S. NATARAJAN,
PHYSICS LETTERS
USING INFRARED
OF SOME CROTONATES
J. GOWRIKRISHNA
Dcpnr~nrr~~r of Physics. hrdim hsrirurc
70 April 1983
BAND SHAPES
and J. SOBHANADRJ
of Tccl~rrolo~. Madras
600
036. fudio
Received 9 Dcccmber 1983;in final foml ?I I;ebruary 1984
Tbc dipole corrclstion function of three esters of crotonic acid have been ccmputrd from the infrared absorption bands. Both short-time and long-time behaviour of the correlation functions are computed and discussed. The correlation times xc also calculated. Thhc short-time behaviour was compared with the correlation functions generated as an even-power series with second and ;ourth moments. They were also compared with the correlation functions of the freely rotating molecule.
1. Introduction
frequency are generally dependent on all of these moments. The first moment can be used to locate the true frequency of the internal transitions. In the solvent-shift studies, this defines the shifted band origin. The second moment of a band is useful for calculating the average molecular rotational kinetic ener,,g. The higher-order momentsgive information about the intermolecular torques. At short times. the correlation function can be written as an even power series of the moments of the absorption band. In this paper, we present the results of the time correlation analysis carried out on the C-O stretch
Band-shape analysis of JR and Raman spectra provides information about the rotational motions of molecules and their intermolecular forces and torques in condensed phases [I-S]. Here the spectrum is considered as the Fourier transform of an appropriate time correlation function. Looking at the spectrum this way, one finds that on inversion one can get the time correlation function as a Fourier integral over the entire spectrum. By this, one can experimentally isolate the short-time and long-time behaviour of the correlation
function.
The
need
for such
[9]
a separation
stems from the fact that while the short-time behaviour of the correlation function may be discussed fairly rigorously in terms of the dynamics of the many-molecule system, at longer times the dynamics become too difficult and one has to rely on statistical arguments to establish the form of the correlation function. The advantage of looking at the spectra in the time-domain in terms of the correlation function instead of attempting to interpret the frequency spectrum directly is due to the reason that the intensity at any particular frequency includes contnbn>ans from the entire time development of the correlation function, that is, both the short- and long-time pars. In the case of a finite spectrum, the spectrum can be characterised uniquely by its moments. Any property of the spectrum such as the frequency at maximum intensity, the half-width, and the intensity at any 0 009-7614/84/S
(North-Holland
03.OCEl Elsevier Science Publishers Physics Publishing Division)
B.V.
and
the asymmetric
out-of-plane
deformation
of
bands of three crotonates in the pure liquids and in solution form. The second and fourth momentswcre cakulated from the band shapes. Also the first moment was determined to locate the shifted band origin. The correlation function behaviour of these compounds is compared with that of the classical ensemble of freely rotating molecules. The pupose of the present study is to understand the effect of the solvent, carbon tetrachloride in this case. on the solute and also to understand the short-rime and longtime behaviour of the molecule using the second and fourth moments calculated from the spectra. the methyl-group
[lo]
2. Experimental
The three compounds,
methyl.
ethyl and propyl 211
CHEMICAL
Volume 106. number 3
crotonates, were prepared and their purity was tested by measuring their boiling points, density and refractive index. The spectra for different concentrations were recorded with a Perkin-Elmer double-beam spectrometer (model PE983) at 27°C. The bands that are selected for the present study are not overlapped by the solvent (CC14) bands. The bands are centered at about 1186 cm- 1 for ethyl and propyl crotonates and at about 1378 cm-l for methyl crotonate. The spectra were recorded for a path length of 0.2 mm.
3. Computational
details
The dipole correlation functions from the expression [ 1 l] (u(O) -U(E)} =~i(w)
cos[(o
were computed
do ,
--w ($1
(1)
= I(w)(Jl(w)
dw) -’
(2)
is the normalised initial-state averaged transition probability at different angular frequencies. I(w) is given by WI
@I = a(4b
11- exp(-k&T)]
,
(3)
where u(o) is the absorption coefficient as a function of the angular frequency and is calculated from [ 131 T = To exp(-o
d) ,
0
where To is the incicient radiation and T is the transmitted radiation for a sample of thickness d. w. in expression (1) is the frequency of the band centre, i.e. the frequency of the vibrational transition of the isolated molecule. This is obtained from the first moment of the band [ 141:
The second and fourth moments [bZ(2) and fi1(4)] were calculated using the relations M(2) 212
=j-I(w)(w
- wo)2 dw ,
M(4) =Ji(o)
(w - w,-J4 dw .
(6)
Using these two, the short-time correlation function is expanded in an even power series as [ 1 1,151
1 - (1/2!)b1(2)t2
+(1/4!)hf(4)t4
+... (7)
The correlation function of a classical ensemble of freely rotating molecules is generally calculated in terms of reduced time units of (I/kT)‘I’. Here I is the moment of inertia, k is the Boltzmann constant and T is the temperature in kelvin. For 3 symmetric top [ 161 (prolate and oblate rotors) the moments of inertia about the three principal axes are considered. The expression used for CH,Cl, [ 171 (prolate rotor) is
(freely rotating)a
= exp[--$kT(l/Ib
where u(r) is the unit vector along the direction of the permanent dipole moment of the molecule at time r and I
20 April 1984
PHYSICS LETTERS
+ l/IC)r2]
.
For an asymmetric top, such as the crotonates considered in this paper, it would be easier to plot exp[-flf(2)t2/2] to represent the free rotor. A computer programme in Fortran TV language for the IBM 3701155 computer has been written to carry out the numerical calculations. The calculations were carried out for time intervals of 0.02 ps, over a total period of 2.0 ps, throughout the band-width, which is about 70-80 cm-l.
4. Results and discussion The time correlation analysis has been carried out on the C-O stretch band (z 1186 cm-l) of ethyl and propyl crotonates and on the asymmetric deformation of the methyl group (== 1378 cm-l) of methyl crotonate. The resultsare shown in figs. 14. In each figure, the correlation variation with 0.02 and 0.1 ps, time intervals are shown. Fig. 1 shows the correlation function variation for the three compounds in pure liquid form and figs. 24 show the concentration dependence. Apart from calculating the time correlation functions at various intervals, the correlation times and second and fourth moments were also calculated. The correlation functions have been calculated for two different time intervals (0.02 and 0.01 ps).
Volume
106, number
3
CHEMICAL
PHYSICS
20 April 1984
LETTERS
8 TIME
tps) (b) ~MCT(1378cri’ ECT (1186cm-1 -PCT (1185cm-’ --Free-rotor
2.0
-
TIMEtps) Fig. 1. Dipole
correlation functions for ethyl, methyl and propyl crotonates in pure liquid form are shown computed infrared absorption band at 1186 cm -’ for the ethyl and propyl crotonates and at 1378 cm -’ for methyl crotonare. ponds to correlation function variation with 0.1 ps time intervals and (b) for 0.02 ps intervals.
One common feature that can be observed in all these figures is that there is 2n initial curvature in the
from the (a) corres-
tributions from various processes to these bands are the same. The correlation functions in the case of
correlation function behaviour which is parabolic in
these two compounds decay faster than that in the
nature_ The time period of this initial curvature is different for different compounds. After this, the decay is essentially exponential.
case of methyl crotonate.This implies that in the ethyl 2nd propyi crotonates, the molecules undergo perturbation earlier t.lnvr in the methyl crotonate molccuie. This is understandable from the structures of rhese
4. I _ h-e
molecules.
liquids
The correlation function decay for the three compounds in pure-liquid form are shown in fig. 1. The correlation function variations in the case of ethyl and propyl crotonates are nearly the same except that it attains a small negative value in the case of propyl crotonate at longer times. This indicates that the con-
4.2. SoiLl tiOlU The correlation function decay for various concentrations of the three compounds in carbon tetrachloride solutions are shown in figs. 21. The correlation functions calculated for a classical ensemble of a freely 213
Volume
-CHEMICAL
106, number 3
20 April 1984
PHYSICS LETTERS
TIME
(ps)
(b)-40% ---
2 0% 60% Free-rotor
TIME (ps) Fig. 2. Dipole correlation function contours. The correlation function and (b) for 0.02 ps time intervals.
rotating
molecule
for methyl crotonate (in CQ) for four different concentrations obtained from the IR band for a freely rotating molecule is aLso shown. (a) corresponds to correlation function for 0.1
are also shown
In the case of methyl ps, the actual correlation
in figs 24.
crotonate, till a time of 1.I0 function is indistinguishable
from th’at of the freely rotating molecule (fig. 1). Later on, due to strong molecular collisions the actual correlation function falls of rapidly compared to that of the free rotor. In the case of ethyl and propyl crotonates, this value is 0.22 and 032 ps. The correlation function values corresponding to these times are O-64,0.79 and 0.67. We can estimate the approximate value of the angle through which the molecule makes free jumps. The actual value of the correlation function where the observed correlation function deviates 214
ps
from that of the free rotor is approximately equal to cos 0 where B is the parameter of interest [ 181. From this relation the angle through which the methyl,ethyl and propyl crotonate molecules make free jumps are obtained as 50°, 3S” and 48” respectively. There have been many reports on such estimations in the literature [ 17,181. It was assumed, in general, that molecular orientational motion occurs through small angles [ 191. Later it was observed that this type of diffusional behaviour does not take place in the case of liquids with small molecules such as Hz [20], CH4 [21] and NH3 1221. Even in the case of larger molecules the rotational steps are observed to be fairly large [23,17].
Volume
106, number
3
CHEMICAL
PHYSICS
20 April
LE’ITERS
1984
(ps)
TIME
&k&4-A+
20% 40%
7
60%
e ---
00%
Free-rotor
TIME (ps) Fig. 3. Dipolc correlation functions for ethyl crotonatc (in CC&) for four different concentrations obtained tours. The correlation function for a freely rotating molecule is also shown. (a) long-time and (b) short-time
As for the effect of the solvent concentration on the solute molecules, there is no effect on methyl crotonate molecules till about 0.16 ps. Similarly for ethyl and propyl crotonates it is 0.06 ps. The calculated correlation times for various concentrations are listed in table 1. The correlation times are generally increasing with increase in solvent concentration_ The correlation function calculated will have contributions from vibrational and rotational rekxation processes of the molecule. In order to separate these two one has to combine the infrared studies with Raman studies. The isotropic bandshape of the Raman scattering contains information about non-orientational motions of the molecule [%I] _
Table 1 Correlation times for various for the three crotonatrs Concentration
a)
(CCL)
100 80 60 40 70 10 a) In volume
from the IR band conbeha\iour.
concentrations
in
ccl4solution
~c methyl
ethyl
propyl
crotonste
croron3te
crotonixe
150 1.70 1.64 1.90 1.45
0.40 0.36 0.37 0.49 0.68 0.69
0.45 0.53 0.52. 0.53 0.87
percentage.
215
Volume 106:number 3
CHEMICAL
PHYSICS LE-ITERS
TIME
TIME
20 April 1984
(ps)
M eeecr -
20% 60% 00%
----
Fresrotor
(ps)
Fig. 4. Dipole correlation functions for propyl crotonaie (in CC&> for four different concentrations obtained from the IR band contours. The correlation function for a freely rotating molecule is also shown. (a) long-time and (b) short-time behaviour.
There are uncertainties in evaluating such correlation functions [IV]. (1) The correct baseline to use is often difficult to select. This difficulty arises due to the asymmetry of the band. (2) The vibrational relaxation processes contribute to the correlation times. (3) The perturbations due to hot bands. One way of avoiding the uncertainty in the baseline is to adjust the experimental second moment to the theoretical value by changing the base line. 4.3. Con-elation function for short times The correlation function is calculated using an evenpower series of the second [b!(2)] and fourth moments 216
[M(4)] for short times [ 1 I]. This way we can separate the short-time behaviour from the long-time behaviour. Substituting the calculated [M(3)] and [M(4)] values in the even-power series, the correlation functions are estimated and compared with the correlation functions calculated from the Fourier integral_ For methyl crotonate both these values agreeing upto a time of 0.9 ps and for ethyl and propyl crotonates upto 0.40 and 0.34 ps. For times higher than this, the neglect of higher-order moments is very much apparent. Since the higher-order moments are much more complicated, the computation of moments is difficult. Moreover, at long times the correlation function behaviour is exponential. So it cannot be generated using the evenpower series.
CHEhlICAL
Volume 106, nunlbcr 3
PHYSICS
From table I, one can see that the correlation times have approximately a linear dependence on solvent concentration. The following equations have been calculated by the least-squares method to represent the solvent concentration dependence of the correlation times (in ps): For methyl crotonate, rc = -0.57
“n + 2.08 _
For ethyl crotonates.
For propyl crotonate,
References [ I] R.G. Gordon, J. Chem. Phys. 44 (1966) 1630. [ 2 1 2. Gburski and W. Szezcpsnski. 5101. Phvs. 40 (1980) 649. [3] M.L. Bansal and A.P. Roy. Mol. Phvs. 38 (1979) 1419. 141 J.K. Vij. C.J. Reid. G.J. Evans, 51. Fermrio rmd Xl.\\‘. Evans, Advan. Mol. Rclau. Interaction Processes 22 (1982) 79. [S 1 S. Ikawa, 2;. Sate zmd M. Kimura. Chem. Phys. 47 (1980) 6.5. [6] J. McConnell, Rotxion brow&n moxion and diclec~ric
[9]
-0.07 xB + 0.56 ,
=
where xB is the solvent 100.
From these equations
1984
theory (Academic Press, New York, 1980). 17 ] W.G. Rorllschild, J. Chem. Phys. 65 (1976) 455. [8] R.G. Gordon. J. Chem. Phys. 39 (1963) 2788.
7, = -o.53_rB + 0.75 .
TC
20 April
LETTERS
concentration
in percentage/
we see that the dependence
calculated for methyl and ethyl crotonatesare parallel. and that their dependence is greater than that of propyl crotonate. With increase in dilution the correlation
of the molecule is retained for a longer time. But the correlation function decay isaway from the free rotor. This can be explained by considering the formation of a cage-like structure by the solvent molecules about the solute molecule. This kind of behaviour has been observed before in many systems like merhylene chlo-
ride molecules in polysterene [ 141, toluene in benzene [X] and pyridine in benzene [26]. From these observations, one can understand the effect of the non-polar solvent (carbon tetrachloride) on the solute molecules. From this study, we conclude that the orirntational motions of these molecules occur through large angles. The effect of the solvent on the solute molecules is clearly seen in this study.
Ados of spectral compounds. 2nd chaIt 5, p 332. [ 101 Atlas of spcctrrrl compounds, 2nd
datn and physical Ed., Vol.
1 (CRC
constsnrs
for organic
Press. Clewland)
dsta and physical constants ior orgonic Ed., Vol. 1 (CRC Press. Cleveland) chart 7. Esters and lactones, pp. 344 ff. [ 1 I ] W.G. Rothschild, J. Chem. Phvs. 49 (1968) 2250. [12j H.B.LevineandG.Bimbaum,Phys. Rev. 154(1967)56. [ 131 T.K.K. Srinivaan. J. Gowrikrishna and J. Sobhansdri, J. Mol. Liquids 26 (1983) 177. [ 141 \V.C. Rothschild, Macromolecules 1 (196s) 43. [ 15.1R.G.Gordon,J.Cbcm.Ph~s.43(1965) 1307. [ 16 1 W.G. Rothschild, J. Chem. Phps. 52 (1970) 6453.
! 171 \v.C. Roghschitd. J. Chcm. Phvs. 13 (1970) 990. [ 181 W.G. Rothschild, G.J. Rosasco and R.C. Livingsron. J. Chem. Phys.61(1975) 1253. [ 191 W.G. Rothschild, J. Chem. Phys.
53 (1970) 3265. [ 201 G.W. Hollernan and G.E. Ewing. J. Chem. Phvs. 47
(1967) 571. 121 l A. Cnbrorrr, R. Bardoux
and A. Chxnberland. Can. J. Chem. 47 (1969) 2915. 1221 P. Datts snd G.M. Bsrrow, J. Am. Chem. Sot. 87 (1965) 3053. [23] \V.G. Rothschild. J. Cbem. Phys. 51 (1969) 5187. [ 241 J.E. Griftiths. in: Vibrational spectra and structure, Vol. 6. ed. J.R. Durig (Elsevier, Amsterdam. 1977). [ 251 W. Reimschussel and H. Abramczyk, Cbem. Phys. Lcricrs 73 (1981) 565. (26 1 J. Gowrikrishn;l, T.K.K. Srinivaszn and J. Sobhanndri. J. Mol. Liquids, to be pubhshcd.
Acknowledgement The authors
are grateful
to Professor
S. Surjit Singh fadi-
for useful discussions and also for experimental ties.
217